using boolean modifiers and shape keys in animation
I think this would probably be a lot easier if you made a dummy object used as subtraction for the Boolean Operation.

Just model a pill-like cylinder object ending in a spherical cap, possibly starting from a UV sphere, then use that in the Boolean operation.



You can then hide it, make it unrenderable, possibly even parented to the real sphere, and use it instead as the Boolean operand, and it should easily simulate the desired effect.